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Connecting quasinormal modes and heat kernels in 1-loop determinants

by Cynthia Keeler, Victoria L. Martin, Andrew Svesko

Submission summary

As Contributors: Andrew Svesko
Arxiv Link: (pdf)
Date accepted: 2020-01-23
Date submitted: 2019-11-15 01:00
Submitted by: Svesko, Andrew
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes.

Ontology / Topics

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Loop models

Published as SciPost Phys. 8, 017 (2020)

Reports on this Submission

Anonymous Report 1 on 2020-1-19 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1811.08433v3, delivered 2020-01-19, doi: 10.21468/SciPost.Report.1460


The strengths are the same as in my previous report. It is the
connection made in this paper of the quasi-normal modes of the BTZ black hole to the the Selberg zeta function.


1. The weakness is again, not exploiting the connection
to a new situation.
2. I also agree with the second referee that, it is not clear that
the connection found by the authors provides a more efficient method to evaluate quasi-normal modes. This would indeed
would have been demonstrated if the authors would have
applied the connection to a new situation.


I have gone through the changes, I agree with the authors
that the generalisation to the higher spin case will involve more
work and it deserves a separate publication.

Also I agree with the comments of the authors, that for g-
handled body geometries, one needs to make a choice of
which cycle which needs to be identified as the thermal circle.
The quasi-normal modes most likely depends on this choice
and this would involve more work.

I am satisfied by the replies of the authors and the
comments inserted in the text.

The article is now suitable for publishing in the journal.

  • validity: high
  • significance: good
  • originality: good
  • clarity: good
  • formatting: good
  • grammar: good

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